Question 1

Which of the following is the domain of the function $$f(x) = \frac{1}{x-7}$$?

Accepted Answer

$$x 
eq 7$$

Question 2

Given $$f(x) = x^2$ + 1$$, what is $$f(-3)$$?

Accepted Answer

$$10$$

Question 3

Simplify $$\sqrt{27} - \sqrt{12}.$$

Accepted Answer

$$3\sqrt{3} - 2\sqrt{3} = \sqrt{3}$$

Question 4

Simplify $$\frac{x^2$ - 6x + 7}{x^2$ - x - 2}.$$

Accepted Answer

Question 5

Solve for $$x$$: $$\log_2$ x = 4.$$

Accepted Answer

$$x = 16$$

Question 6

Solve for $$x$$: $$\frac{4x}{x+2} = 2.$$

Accepted Answer

$$x = 2$$

Question 7

Solve the quadratic equation $$2x^2 - 4x = 0$.

Accepted Answer

$$x = 0 or$$ $$x = 2$$

Question 8

Which of the following is the correct simplification of $$\log_3$ 81$$?

Accepted Answer

$$4$$

Question 9

Find the vertex of the parabola $$f(x) = x^2$ - 1x + 6.$$

Accepted Answer

$$(0.5, 5.75)$$

Question 10

David labels 144 tins in 6 days. At this rate, how many tins would he label in 15 days?

Accepted Answer

$$360$$

Question 11

Suppose $$10,000 is $$invested at $$5\%$$ interest compounded monthly. The amount after $$t$$ years is $$A(t) = 10000(1.004167$$)^{12t}$$. What is the amount after 5$ years?

Accepted Answer

$$12,834.59$$

Question 12

How long will it take to accumulate $$15,000 in $$the account described by $$A(t) = 10000(1.004167$$)^{12t}$$?

Accepted Answer

$$8.11$$ years

Question 13

Which graph below best represents $$f(x) = e$$^{x}$$?

Accepted Answer

A graph that passes through $$(0,1)$$ and increases rapidly for $$x \u003e 0$$

Question 14

Express $$\log_a r + \frac{1}{2} \log_a s - 3 \log_a t as a $$single logarithm.

Accepted Answer

$$\log_a \left( \frac{r \sqrt{s}}{t^3$} \right)$$

Question 15

Solve the equation $$9^{x+4}$$ = $$27^{x+1}.$$

Accepted Answer

$$x = -1$$

Question 16

Find the axis of symmetry for the parabola $$f(x) = x^2$ - x + 6.$$

Accepted Answer

$$x = 0.5$$

Question 17

If $$f(x) = x^2$ - x + 6$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$5.75$$

Question 18

Solve for $$x$$: $$f(x) = 8$$ where $$f(x) = x^2$ - x + 6.$$

Accepted Answer

$$x = 2 or$$ $$x = -3$$

Question 19

Which of the following is the correct simplification of $$\log_2$ 8$$?

Accepted Answer

$$3$$

College Algebra Final Exam Study Guide

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